We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic convex risk measures. We employ a time-consistent dynamic programming principle to determine the value of a particular policy, and develop policy gradient update rules that aid in obtaining optimal policies. We further develop an actor–critic style algorithm using neural networks to optimize over policies. Finally, we demonstrate the performance and flexibility of our approach by applying it to three optimization problems: statistical arbitrage trading strategies, financial hedging, and obstacle avoidance robot control.